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POVM construction: a simple recipe with applications to symmetric states

Sirsi, Swarnamala; Bharath, Karthik; Shilpashree, S.P.; Rao, H.S. Smitha

Authors

Swarnamala Sirsi

Karthik Bharath karthik.bharath@nottingham.ac.uk

S.P. Shilpashree

H.S. Smitha Rao



Abstract

We propose a simple method for constructing POVMs using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construction on the n+1-dimensional subspace of the 2n-dimensional Hilbert space of n qubits comprising the permutationally symmetric states. Using the notion of vectorization, the constructed POVMs are interpretable as projection operators in a higher-dimensional space. We then describe a method to physically realize the constructed POVMs for symmetric states using the Clebsch-Gordan decomposition of the tensor product of irreducible representations of the rotation group. We illustrate the proposed construction on a spin-1 system, and show that it is possible to generate entangled states from separable ones.

Journal Article Type Article
Journal International Journal of Quantum Information
Print ISSN 0219-7499
Electronic ISSN 1793-6918
Publisher World Scientific
Peer Reviewed Peer Reviewed
Volume 15
APA6 Citation Sirsi, S., Bharath, K., Shilpashree, S., & Rao, H. S. (in press). POVM construction: a simple recipe with applications to symmetric states. International Journal of Quantum Information, 15, doi:10.1142/S0219749917500423
DOI https://doi.org/10.1142/S0219749917500423
Keywords Permutationally symmetric states; Projection operators; POVM
Publisher URL http://www.worldscientific.com/doi/abs/10.1142/S0219749917500423
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information Electronic version of an article published as Swarnamala Sirsi et al, Int. J. Quantum Inform. 15, 1750042 (2017) [12 pages] https://doi.org/10.1142/S0219749917500423 copyright World Scientific Publishing Company http://www.worldscienti....1142/S0219749917500423

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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